Question
Show that $\alpha+\beta=\beta+\alpha$ for all $\alpha, \beta \in \mathbf{C}.$
Step 1
Let $\alpha = a + bi$ and $\beta = c + di$, where $a, b, c, d \in \mathbf{R}$ and $i$ is the imaginary unit with the property that $i^2 = -1$. Show more…
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If $A=\left[\begin{array}{ll}a & b \\ b & a\end{array}\right]$ and $A^{2}=\left[\begin{array}{ll}\alpha & \beta \\ \beta & \alpha\end{array}\right]$, then show that $\alpha=a^{2}+b^{2}, \beta=2 a b$.
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